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Secondary 1 Mathematics Semestral Assessment 2 (End of Year) Paper 4

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Questions

TuitionGoWhere Exam Practice (AI) — SA2 Mathematics Secondary 1

School: TuitionGoWhere Secondary School (AI)
Subject: Mathematics
Level: Secondary 1
Paper: SA2 Practice Paper (Version 4 of 5)
Duration: 60 minutes
Total Marks: 60
Name: ________________________
Class: ________
Date: ____________

Instructions:

Answer all questions in the spaces provided.
Show your working clearly for all calculation questions.
Use a calculator where necessary.
Write your answers in the units given or as requested.

Section A: Numbers and Operations (Questions 1–5) — [15 marks]

1. [3 marks] Express 252 as a product of its prime factors. Hence, find the highest common factor (HCF) of 252 and 180.

2. [2 marks] Evaluate $\frac{3}{4} - \left(-\frac{5}{8}\right) + 1.25$ . Give your answer as a decimal.

3. [3 marks] Round 0.07486 to (i) 2 decimal places, (ii) 3 significant figures. State the difference between the two rounded values.

4. [3 marks] Represent the inequality $-2x \leq 6$ on the number line below. State the solution set.

Diagram for Q4 (SEC1 Maths)

Generated diagram for Q4.

5. [4 marks] A shop sells a jacket at $96 after a 20% discount. Find the original price. Hence, find the percentage increase if the price is later marked up to $120.

Section B: Ratio and Proportion (Questions 6–12) — [21 marks]

6. [2 marks] Simplify the ratio $1.2 : 0.8 : 2.4$ to its simplest form.

7. [3 marks] The ratio of boys to girls in a class is $3 : 5$ . If there are 24 boys, how many girls are there? If 4 more girls join, what is the new ratio of boys to girls in simplest form?

8. [3 marks] A recipe for 5 cakes requires 300 g of flour and 200 g of sugar. How much flour and sugar are needed for 8 cakes? Give your answers in grams.

9. [3 marks] The number of red marbles is $\frac{2}{3}$ the number of blue marbles. If there are 18 blue marbles, find the ratio of red to blue to total marbles in simplest form.

10. [3 marks] A map is drawn to a scale of 1 : 25 000. Two towns are 8 cm apart on the map. Find the actual distance in kilometres.

11. [3 marks] The ratio of money saved by Ali, Ben and Cai is $4 : 5 : 6$ . If Ben saves $45, find the total amount saved by the three boys.

12. [4 marks] The number of stickers Lina has is twice that of Mina. After Lina gives away 30% of her stickers, she has 14 fewer stickers than Mina. How many stickers did Mina have at first?

Section C: Percentage, Rate and Speed (Questions 13–20) — [24 marks]

13. [2 marks] Find the percentage increase in temperature from 20°C to 25°C.

14. [3 marks] A laptop costs $800. Its price increases by 15% in January and then decreases by 10% in June. Find the final price.

15. [3 marks] In a survey of 80 students, 28 chose badminton as their favourite sport. Calculate the percentage of students who chose badminton.

16. [3 marks] Water flows into a tank at a rate of 500 mL per second. How many 2 L bottles can be filled in 10 minutes?

17. [3 marks] A car travels 240 km in 3 hours. Find its average speed in km/h. If it travels the next 160 km at 80 km/h, find the average speed for the whole journey.

18. [3 marks] The price of a book is $24. This is 20% less than its original price. Find the original price.

19. [3 marks] A worker is paid $15 per hour. If he works 42 hours in a week, find his total wage. If his wage increases by 8%, what is his new weekly wage?

20. [4 marks] The ratio of boys to girls in a club is $2 : 3$ . The number of boys increases by 50% and the number of girls decreases by 20%. Find the new ratio of boys to girls in simplest form.

End of Paper

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Answers

TuitionGoWhere Exam Practice (AI) — SA2 Mathematics Secondary 1 (Version 4) Answer Key

Total Marks: 60

Section A: Numbers and Operations (15 marks)

Q1 [3 marks]
Prime factorisation of 252:
$252 = 2 \times 126 = 2 \times 2 \times 63 = 2^2 \times 3 \times 21 = 2^2 \times 3^2 \times 7$
Prime factorisation of 180: $180 = 2^2 \times 3^2 \times 5$
HCF = product of lowest powers of common primes = $2^2 \times 3^2 = 4 \times 9 = 36$
Marks: 1 for 252 factors, 1 for 180 factors (or implied), 1 for HCF = 36.

Q2 [2 marks]
$\frac{3}{4} = 0.75,\ -\left(-\frac{5}{8}\right) = +0.625,\ 1.25$
$0.75 + 0.625 + 1.25 = 2.625$
Marks: 1 for converting fractions, 1 for final answer 2.625.

Q3 [3 marks]
(i) 2 dp: 0.07
(ii) 3 sf: 0.0749
Difference = $0.0749 - 0.07 = 0.0049$
Marks: 1 each for (i), (ii), difference.

Q4 [3 marks]
$-2x \leq 6 \Rightarrow x \geq -3$ (divide by -2, reverse sign)
Number line: closed circle at -3, arrow right. Solution set: $\{x : x \geq -3\}$
Marks: 1 for solving, 1 for correct circle, 1 for arrow/direction.

Q5 [4 marks]
Discounted price = 80% of original → $0.8P = 96 \Rightarrow P = 96/0.8 = 120$
Original = $120. Marked up to $120 → increase = 0, so 0%.
Marks: 2 for original price, 2 for percentage increase = 0%.

Section B: Ratio and Proportion (21 marks)

Q6 [2 marks]
Multiply by 10: $12 : 8 : 24$ ; divide by 4 → $3 : 2 : 6$
Marks: 1 for clearing decimals, 1 for simplest form.

Q7 [3 marks]
$3 : 5 = 24 : g \Rightarrow g = 24 \times 5 / 3 = 40$ girls.
New: 24 boys, 44 girls → $24 : 44 = 6 : 11$
Marks: 1 for girls, 1 for new ratio setup, 1 for simplest form.

Q8 [3 marks]
Flour per cake = $300/5 = 60$ g → 8 cakes = $480$ g
Sugar per cake = $200/5 = 40$ g → 8 cakes = $320$ g
Marks: 1.5 each ingredient.

Q9 [3 marks]
Red = $\frac{2}{3} \times 18 = 12$ . Total = $12+18=30$ . Ratio $12 : 18 : 30 = 2 : 3 : 5$
Marks: 1 each for red, total, simplified ratio.

Q10 [3 marks]
Actual = $8 \times 25000 = 200000$ cm = $2000$ m = $2$ km
Marks: 1 for cm, 1 for m, 1 for km.

Q11 [3 marks]
Ben = 5 units = $45 → 1 unit = $9. Total = $15 \times 9 = \$ 135$
Marks: 1 for unit, 2 for total.

Q12 [4 marks]
Let Mina = $m$ , Lina = $2m$ . Lina after = $0.7 \times 2m = 1.4m$ .
$1.4m = m - 14 \Rightarrow 0.4m = 14 \Rightarrow m = 35$
Marks: 1 setup, 1 equation, 1 solve, 1 answer 35.

Section C: Percentage, Rate and Speed (24 marks)

Q13 [2 marks]
Increase = $25-20=5$ . % = $5/20 \times 100 = 25\%$
Marks: 1 change, 1 percentage.

Q14 [3 marks]
Jan: $800 \times 1.15 = 920$ . June: $920 \times 0.9 = 828$
Marks: 1.5 each step.

Q15 [3 marks]
$28/80 \times 100 = 35\%$
Marks: 1 fraction, 1 calc, 1 %.

Q16 [3 marks]
10 min = 600 s. Total = $500 \times 600 = 300000$ mL = 300 L.
Bottles = $300 / 2 = 150$
Marks: 1 time, 1 total vol, 1 bottles.

Q17 [3 marks]
First: $240/3 = 80$ km/h. Total dist = 400 km, total time = $3+2=5$ h → $400/5 = 80$ km/h
Marks: 1 first, 1 second time, 1 average.

Q18 [3 marks]
$0.8P = 24 \Rightarrow P = 30$
Marks: 1 equation, 2 answer.

Q19 [3 marks]
Wage = $15 \times 42 = 630$ . New = $630 \times 1.08 = 680.40$
Marks: 1.5 each.

Q20 [4 marks]
Boys = $2u \to 3u$ ; Girls = $3u \to 2.4u$ . Ratio $3 : 2.4 = 30 : 24 = 5 : 4$
Marks: 1 each transformation, 2 simplify.

End of Answer Key